confuse to find power factor

[andi21]

1. The problem statement, all variables and given/known data
An induction motor load of 2000 kVA has power factor 0.80 lagging. Synchronous motors totaling 500 kVA are added an operated at a leading power factor. If the overall power factor is then 0.90 lagging, what is the power factor of the synchronous motors?


2. Relevant equations
i use power triangle to solve the values of powers in induction motor..


3. The attempt at a solution
i have solve the reactive power = 1200 kvar ; p=1600 kw..
i am confuse how to use the total power factor... in need to find the real power in the synchronous motors... in order to find the power factor of the synchronous motors...

 

[FvM]

The problem is about adding vectors and can be best most easily solved with ruler and compasses. Imagine the 500 kVA locus as a circle.

 

[andi21]

I'm sorry. I don't get your point.

 

[FvM]

I don't get your point.

The ask your text book.

I'm talking about a graphical solution. Draw the 2000 kVA vector, draw a PF 0.9 line. You don't know the actual PF of the 500 kVA load, but you know the vector length, that adds to the 2000 kVA vector.

 

[Prototyp_V1.0]

Go get Geogebra and draw like this: